California Educational Research Association Disneyland Hotel – Anaheim, CA December 1, 2011 Terry Vendlinski Julia Phelan Improving Middle School Math Instruction: Formative Assessment, PD and Big Ideas

2 / 11 Background Math instruction seldom builds on the prior knowledge of students and doesn’t account for student misconceptions. Math is often presented as a list of facts to be memorized and procedures to be implemented. Students often see these facts and procedures as random or disorganized. Students have little understanding of how math relates to or is useful in the “real” world.

3 / 11 Method Organize instruction around key foundational ideas (unlike many textbooks) Develop formative assessments, instructional materials and professional development around these foundational ideas. Measure the way teachers conceptually organize content and choose exemplary problems to illustrate a concept. Compare pre / post maps to experts

4 / 11 Concept Maps Links applies to can represent is a property of type of used to Concepts Additive Identity Additive Inverse Distributive Property Equivalence Factoring Fractions

5 / 11 Exemplary Problems Solve for the unknown: c = 40 Evaluate the expression y + 3 when y = 2 The two triangles are similar, what is the length of side AB? Solve for the unknown: 15=  15

6 / 11 Knowledge (Concept) Map Example Can represent repeated undoes Division Multiplication Addition Subtraction Find the mean of 3, 6, 9, 15 1 Find the product of 12 x 3 2

7 / 11 Our Research Questions Through professional development, can teachers change their conceptual organization of the mathematics domain they teach to become more like experts? Do teachers in different grades respond differently to professional development? Do teachers with different levels of experience respond differently to professional development?

8 / 11 The study 144 teachers from seven public school districts in Southern California and Arizona. 8 + hours of professional development in three conceptual areas that involved conceptual understanding and analysis of student work. Phased-in approach from 6 th to 7 th to 8 th grade teachers. Randomized Control Trial using both within and between-school groups.

9 / 11 Do teachers change in their ability to organize math concepts? 6 th grade teachers showed marginally significant differences in their ability to organize math concepts after one year of PD 6 th grade teachers showed significant differences in their ability to connect problems and concepts after two years of PD. 7 th grade teachers showed significant differences in their ability to organize math concepts after two years of PD.

10 / 11 Conclusions The way teachers organize conceptual thinking does change, but the rate appears to differ by grade. The way teachers connect problems and concepts appears to take longer to develop. These changes also appear to be related to experience. Sixth grade teachers had significantly more math teaching experience and MS math teaching and were significantly more likely to have a single subject credential.

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